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alukav5142 [94]
2 years ago
6

Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real

number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.
Mathematics
1 answer:
garik1379 [7]2 years ago
5 0

The complete question is

"Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.

0 = 2x^2 – 7x – 9

0 = 4x^ 2 – 3x – 1

The quadratic equations that have real number solutions are; 4x^2 – 3x – 1, and 2x^2 – 7x – 9.

<h3>What is the formula for Discriminant?</h3>

The formula for finding the discriminant is

b^2 - 4ac

The solution contains the term \sqrt{b^2 - 4ac} which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

For the quadratic equation 2x^2 - 7x - 9

b^2 - 4ac

= (-7) ^2 - 4( 2) ( -9)\\\\= 49 + 72 = 121

This equation has two real number solutions.

For the quadratic equation 4x^ 2 - 3x- 1

b^2 - 4ac

= (-3) ^2 - 4( 4) ( -1)\\\\= 9 + 16 = 25

This equation will have two real number solutions.

Learn more on discriminant here:

brainly.com/question/1537997

#SPJ1

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the name Joe is very common at a school in one out of every ten students go by the name. If there are 15 students in one class,
kumpel [21]

Using the binomial distribution, it is found that there is a 0.7941 = 79.41% probability that at least one of them is named Joe.

For each student, there are only two possible outcomes, either they are named Joe, or they are not. The probability of a student being named Joe is independent of any other student, hence, the <em>binomial distribution</em> is used to solve this question.

<h3>Binomial probability distribution </h3>

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • One in ten students are named Joe, hence p = \frac{1}{10} = 0.1.
  • There are 15 students in the class, hence n = 15.

The probability that at least one of them is named Joe is:

P(X \geq 1) = 1 - P(X = 0)

In which:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.1)^{0}.(0.9)^{15} = 0.2059

Then:

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2059 = 0.7941

0.7941 = 79.41% probability that at least one of them is named Joe.

To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377

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Step-by-step explanation:

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The Median is the middle value.

Arrange the numbers in order from smallest to largest:


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Since there is an even number, the median is found by adding the 2 middle numbers and dividing by 2.

Median for Seattle: 40.30 + 45.79 = 86.09 / 2 = 43.045


Now do the same for Las Vegas:

2.33, 3.72, 3.84, 4.11, 5.62, 8.79

Median for Las Vegas: 3.84 + 4.11 = 7.95 / 2 = 3.975


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